Question

Решить показательное уравнение 2^x^2-1-3^x^2=3^x^2-1-2^x^2+2

Answer 1

2^( x^2 - 1 ) - 3^x^2 = 3^( х^2 - 1 ) - 2^( х^2 + 2 )
2^( х^2 - 1 ) + 2^( х^2 + 2 ) = 3^( х^2 - 1 ) + 3^х^2
2^х^2•( ( 1/2 ) + 4 ) = 3^(х^2)•( ( 1/3 ) + 1 )
2^х^2•( 4 1/2 ) = 3^х^2•( 1 1/3 )
( 2/3 )^х^2 = 1 1/3 : 4 1/2
1 1/3 : 4 1/2 = 4/3 : 9/2 = 8/27
( 2/3 )^х^2 = 8/27
( 2/3 )^х^2 = ( 2/3 )^3
Х^2 = 3
Х1 = V 3 ; X2 = - V 3